U.S. Pat. No. 4,079,759 discloses a braking device for a weft yarn store, the device comprising a ring which has a resilient insert and which is movable axially towards the drum of the store. A bent lever acts by way of a cam drive to move the brake disc towards the drum, the kinetic energy of the disc being dissipated when the disc impacts the drum periphery. The resulting shock is reduced by the resilient insert but the clamping of the weft yarn between the drum periphery and the brake disc is abrupt. The resilient insert can compensate for errors of alignment between the drum axis and the brake disc axis; however, in this case different surface pressures arise in the contact zone so that the braking of the weft yarn varies with its position on the drum periphery. Consequently, weft yarn lengths may vary between consecutive picks.